Question

write which solid has a greater volume: cone with a base radius of 7 centimeters and a height of 28 centimeters or a pyramid with base area of 154 square centimeters and height of 28 centimeters? explain your reasoning. the cone has a much greater volume select choice the cone and pyramid have nearly the same volumes the pyramid has a much greater volume the cone has a much greater volume. cone: the area of the base is approximately 154 square centimeters, so (vapprox\frac{1}{3}() centimeters. the volume of the pyramid is greater by such a large amount that we

Explanation:

Step1: Calculate cone base - area

The formula for the area of a circle (cone - base) is $A=\pi r^{2}$. Given $r = 7$ cm, then $A=\pi\times7^{2}=49\pi\approx49\times3.14 = 153.86\approx154$ square centimeters.

Step2: Calculate cone volume

The formula for the volume of a cone is $V_{cone}=\frac{1}{3}Ah$, where $A$ is the base - area and $h$ is the height. Substituting $A\approx154$ square centimeters and $h = 28$ centimeters, we get $V_{cone}=\frac{1}{3}\times154\times28=\frac{4312}{3}\approx1437.33$ cubic centimeters.

Step3: Calculate pyramid volume

The formula for the volume of a pyramid is $V_{pyramid}=\frac{1}{3}Ah$, where $A$ is the base - area and $h$ is the height. Given $A = 154$ square centimeters and $h = 28$ centimeters, then $V_{pyramid}=\frac{1}{3}\times154\times28=\frac{4312}{3}\approx1437.33$ cubic centimeters.

Answer:

The cone and pyramid have nearly the same volumes